Problem: Emily is 40 years older than Omar. Eighteen years ago, Emily was 5 times as old as Omar. How old is Omar now?
Solution: We can use the given information to write down two equations that describe the ages of Emily and Omar. Let Emily's current age be $e$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $e = o + 40$ Eighteen years ago, Emily was $e - 18$ years old, and Omar was $o - 18$ years old. The information in the second sentence can be expressed in the following equation: $e - 18 = 5(o - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to use our first equation for $e$ and substitute it into our second equation. Our first equation is: $e = o + 40$ . Substituting this into our second equation, we get the equation: $(o + 40)$ $-$ $18 = 5(o - 18)$ which combines the information about $o$ from both of our original equations. Simplifying both sides of this equation, we get: $o + 22 = 5 o - 90$ Solving for $o$ , we get: $4 o = 112$ $o = 28$.